Spatial Frequency, Bandwidth, and Resolution

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Abstract
When Fourier methods are used to predict the response of an imaging system to very small objects, the concept most directly related to the size of the object or its image is not spatial frequency, but bandwidth. The importance of this distinction is easily demonstrated, using the convolution theorem and the properties of Dirac delta-functions. For example, it is shown that the contrast of the standard three-bar target is not reduced to zero when its number of “lines/mm” equals the high-frequency cutoff of the appropriate transfer function. Misleading conclusions can be avoided by using the correct Fourier integral representation of the object, instead of the series approximation.

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